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Normally Ordered Quantum Gate Operators for Continuum Variables as Images of Classical Transforms

FANHong-Yi, LUHai-Liang

We derive normally ordered quantum gate operators for continuum variables by mapping classical transforms onto Fock space. Successive gate operations can be treated in a unified way that is using the technique of integration within an ordered product of operators.

理论物理通讯：英文版Jan 1, 20030 citations

General Formalism for Mapping of Two-Mode Classical Canonical Transformations to Quantum Unitary operators

Hong-Yi Fan

Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product" technique, and the mapping is manifestly apparent in the derivation. New generalized coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed.Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product" technique, and the mapping is manifestly apparent in the derivation. New generalized coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed.

Communications in Theoretical PhysicsApr 1, 19925 citations

Quantum-Mechanical Unitary Operators Gained via Integrations over a Type of Ket-Bra Operators

Fan Hong-Yi

Applying the technique of integration within ordered product (IWOP) to a type of ket-bra operators which are in integral form in coordinate representation, we derive unitary normally ordered quantum-mechanical images of real symmetric transformations in classical coordinate space, which provide us with a convenient approach to constructing the corresponding coherent states. Some examples showing the physical applications of this kind of unitary images are presented.

Europhysics Letters (EPL)Jan 21, 19922 citations

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

Fan, Hong-Yi,  Fu +1 more

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.

理论物理通讯：英文版Jan 1, 20060 citations

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

Fan Hong-Yi, Liang Fu

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.

Communications in Theoretical PhysicsAug 1, 20062 citations

Simple derivation of the explicit forms of quantum-mechanical fundamental representations

Ye‐Jun Xu, Xiu-Chun Ding, Ji-Zhu Peng +1 more

By finding that the projection operators of the basic quantum mechanical representations can be written as operator delta functions, we derive the explicit forms of quantum-mechanical fundamental representations in Fock space by directly carrying out the integrals within the normally ordered product of operators.

American Journal of PhysicsApr 21, 20211 citation

Normally Ordered Quantum Gate Operators for Continuum Variables as Images of Classical Transforms

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Normally Ordered Quantum Gate Operators for Continuum Variables as Images of Classical Transforms

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